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Hopf Bifurcation From Viscous Shock Waves

Sandstede, Bjorn and Scheel, Arnd (2008) Hopf Bifurcation From Viscous Shock Waves SIAM Journal on Mathematical Analysis, 39 (6). pp. 2033-2052.


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Using spatial dynamics, we prove a Hopf bifurcation theorem for viscous Lax shocks in viscous conservation laws. The bifurcating viscous shocks are unique (up to time and space translation), exponentially localized in space, periodic in time, and their speed satisfies the Rankine– Hugoniot condition. We also prove an “exchange of spectral stability” result for super- and subcritical bifurcations and outline how our proofs can be extended to cover degenerate, over-, and undercompressive viscous shocks.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Scheel, Arnd
Date : 1 January 2008
DOI : 10.1137/060675587
Additional Information : Bjorn Sandstede and Arnd Scheel (2008). Hopf bifurcation from viscous shock waves. <i>SIAM Journal on Mathematical Analysis,</i> Vol. 39, No. 6, pp. 2033-2052. Copyright 2008 Society for Industrial and Applied Mathematics. Click <a href=>here</a> to access the journal's webpage.
Depositing User : Mr Adam Field
Date Deposited : 27 May 2010 14:40
Last Modified : 31 Oct 2017 14:01

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